A1 The function f(x) is defined by f(x) = { { 1 1- ½½|x| for |x| ≤ 2 for |x| >2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f'] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = sin² k k2 dk = π. 0, to show (1)

Evaluate the function when x = 1, 3 and 3 3 1) f (x) 3D х' + 2x — 3 -

Differentiate. Find f'(t) for f(x) O 17 (2x-7)² O (2x-7)2 O 17 (3x - 2)2 (3x - 2) wwwww. 3x-21

Let f(x) = (3x + 7)(3x2 + 2)8. Compute f'(x).

Please show me the steps for f'''(x).  Thank you!

Find the linearization L(x)  of the function f(x) = x^4 -2x^2+3  at  x =0.

3. Let f (x) = (3x2 + 1)?. Find f'(x)in 3 different ways by following the instructions below in parts a, b and c: a) Algebraically multiply out the expression for f (x) and expand, then take the derivative. b) View f (x) as (3x? +1)(3x2 + 1) and use the product rule to find f' (x). C) Apply the chain rule directly to the expression f (x) = (3x² + 1)?. d) Are your answers in parts a, b, c the same? Why or why not?